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The 500 students in a class took an examination. Sco

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The 500 students in a class took an examination. Sco [#permalink] New post 22 Aug 2017, 02:16
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57% (01:41) correct 42% (02:02) wrong based on 14 sessions


The 500 students in a class took an examination. Scores were given on an inte­ger scale of 0-100. Jamal's score was 2 standard deviations above the mean score on the examination, and Charlie's score was at exactly the 5th percentile. The distribution of exam scores was approximately normal. Which of the fol­lowing statements must be true?

Indicate all such statements.

❑ Jamal scored closer to the mean than Charlie.

❑ More than 400 students achieved scores less than or equal to Jamal's score and greater than or equal to Charlie's score.

❑ Fewer than 450 students achieved scores less than or equal to Jamal's score and greater than or equal to Charlie's score.

❑ At least one other person received the same score as Charlie.

[Reveal] Spoiler: OA
B,D
[Reveal] Spoiler: OA

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Re: The 500 students in a class took an examination. Sco [#permalink] New post 23 Apr 2018, 19:00
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A:
You need to know that in a normal curve, the mean is exactly at the 50%ile, 1 standard deviation above the mean is 34%ile above that, and 2 standard deviations above the mean is 14%ile above that. In other words, 2 standard deviations above the mean is around 98%ile. Since Jamal is therefore at 98%ile and Charlie as at 5%ile, Charlie is closer to the mean and this answer is out.


B:
If Charlie is 5%ile, then he performed better than 5% of the total, or 25 people. Since Jamal is 98%ile, he performed better than 98% of the students, meaning about 2% of them, about 10 students, performed better than him. Since only about 35 people out of 500 performed either better or worse than them, 465 must have performed equal to Charlie or above or equal to Jamal or below, so we can see that this answer must be true.

C:
From the last answer choice, we know that we're looking at 465 people, which is well above 450, so this one is out.

D:
Since there are 500 students, every percentile must contain 5 students. The key to this one is the word "exactly". Since the 5th percentile falls between the 25th and 26th student, the 5th percentile itself is the average of the 25th and 26th students' scores. Since the scores are given in integers, if you average two of them, you'll either get an integer, or something that ends in a .5. But since Charlie couldn't have gotten a score that ends in a .5, this scenario is out.

What if the 25th lowest student had scored a 20 and the 26th lowest had gotten a 22? Then the 5th percentile would be 21, but since nobody actually got that score, this scenario is impossible.

The only way Charlie could've gotten exactly the 5th percentile is if the 25th and 26th lowest people got the same score, in which case the average of the two of them equals both of them. Thus, D is in.
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Re: The 500 students in a class took an examination. Sco [#permalink] New post 24 Apr 2018, 01:45
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Amazin explanation. As usual.

I missed it.
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Re: The 500 students in a class took an examination. Sco [#permalink] New post 28 Jul 2018, 01:48
Carcass wrote:
Amazin explanation. As usual.

I missed it.



Hello Carcass. Charlie score is at 5th percentile, which means p5. To find p5, we have to follow those steps:

1: position of p5 is L = 5 * (501)/100 = 25.05
2: M = 25
3: P5 = X25 + (25.05-25)(26-25) = 25.05

I don't understand exactly how D is resolved! I just did the previous logic while i was trying to approach for a solution.
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Re: The 500 students in a class took an examination. Sco [#permalink] New post 29 Jul 2018, 13:24
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Avraheem wrote:

Hello Carcass. Charlie score is at 5th percentile, which means p5. To find p5, we have to follow those steps:

1: position of p5 is L = 5 * (501)/100 = 25.05
2: M = 25
3: P5 = X25 + (25.05-25)(26-25) = 25.05

I don't understand exactly how D is resolved! I just did the previous logic while i was trying to approach for a solution.


Hi,

Could you please clarify what you mena by X25 and M.

Percentile score is that score which divides the highest value in the previous bracket and the lowest value in the next %tile bracket. For example 1% means the score of the 5th and 6th student averaged.


So suppose we have the following score card


Student Rank:
1...2...3...4...5...6...7...8...9...10...11...12

Score:
12..14..14..15..15..16..17..17..17..18..18..19

1%ile score in the case above is 15.5. No one gets exactly one percentile. However 2%tile score is 18. Student number 10 and 11 both have that score.

In order to get an integer percentile you must have the last member of previous bracket and the first member of current bracket with thw same score.

Hence atleast one other guy must have scored the same points as charlie has an integer value of percentile.
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Re: The 500 students in a class took an examination. Sco   [#permalink] 29 Jul 2018, 13:24
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